From VZW's Global Services' interactive planner for Bermuda -
You can use the iPhone 4 - for voice, text and data in all selected countries. Before you travel, contact Verizon Wireless by dialing *611 from your wireless device or (800)922-0204 from any phone to enable international roaming.
Location Bermuda
Voice Rate $1.99/min. (plus applicable taxes & fees, etc.)
Global Data Plan $25/100MB
Pay as you Go data rate $0.020/KB
Text Rate $0.50 send $0.05 receive
Data Network CDMA
Voice Network CDMA
iPhone 4 Tech CDMA
If you can keep in touch for 4 days via Text Messaging, it can be done inexpensively - incoming is 5 cents and 50 cents from Bermuda to US. Just make sure you turned off data roaming on the iPhone 4.
If someone you know has an old AT&T "dumb" tri-band (quad-band is ideal) phone that's unlocked, you can pickup a local BDA prepaid Sim card, and get services while you are there - maybe more challenging for you. If so, prepaid calling card from a pay phone is your best option - as using it to call from a hotel phone might still incur local access surcharges, depending on your stay's. TBI Calling Card is the one to ask for.
More details - here -
http://www.bermuda-attractions.com/bermuda_0001cd.htm